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Uncertainties and errors, graphical techniques - class-XI

Description: uncertainties and errors, graphical techniques
Number of Questions: 45
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Tags: measurement and data processing and analysis chemistry basic concepts of chemistry some basic concepts of chemistry moles and equations stoichiometry introduction to analytical chemistry
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Given the numbers $786$, $0.786$ and $0.0786$. The number significant figures for the numbers is :

  1. $3$, $4$ and $5$ respectively

  2. $3$, $3$ and $3$ respectively

  3. $3$, $3$ and $4$ respectively

  4. $3$, $4$ and $4$ respectively


Correct Option: B

How many significant figures are present in $7 \times 2.232$?

  1. $5$

  2. $3$

  3. $4$

  4. $1$


Correct Option: A
Explanation:

$7 \times 2.232=15.624$

Number of significant figures= $5$

How many significant digits does the measurement $124.04g$ possess?

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$


Correct Option: E
Explanation:

The number of single digits that are important in the coefficient of an expression in scientific notation is termed as significant number.

The significant digits in the given number are $1,2,4,0$ and $4$. Therefore, $5$ significant digits are there in the number $124.04g$.

How many significant digits does the measurement $0.0384g$ possess?

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$


Correct Option: C
Explanation:

The significant digits in the number $0.0384g$ are $3,8$ and $4$. Therefore, the number of significant digits are $3$.

Which of the following numbers has 1 significant figure?

  1. 0.060

  2. 0.60

  3. 6.0

  4. 60


Correct Option: D
Explanation:

There are three rules on determining how many significant figures are in a number: Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant.


Hence, only option D has one significant figure and all others have 2 significant figures.

Hence, the correct option is $\text{D}$

All of the following are good laboratory practices except_________.

  1. Wait for a hot object to cool before weighing it.

  2. Rinse a burette with the solution that will be used to fill the times

  3. Wear goggles at all times

  4. Return unused chemicals to the reagent bottles

  5. To dilute $H _2SO _4$, pour it into water slowly.


Correct Option: A
Explanation:

We use different equipment to cool the object, before weighting it which save time.

Round 984 liters to 2 significant digits.

  1. $1.00\times10^3$ liters

  2. 1000 liters

  3. 900 liters

  4. 980 liters


Correct Option: D
Explanation:

$\text{980 have two non-zero digits ie. with significant figure is 2.}$

The result of the operation 2.5 X 1.25 should be which of the following on the basis of significant figures?

  1. 3.125

  2. 3.13

  3. 3.1

  4. 31.25


Correct Option: C
Explanation:
$2.5 \times 1.25 = 3.125$

The rule says: Answer to a multiplication or division should be rounded off to a same number of significant figures as possessed by the least precise term in the calculation.

Since $2.5$ has least numbers of significant figure i.e.two, thus, the result should have 2 significant figure i.e. $ 3.1$
option C is correct

Each side of a cube is measured to be $7.203$ m. What is the volume of the cube to appropriate significant figure?

  1. $373.7m^3$

  2. $311.3 m^3$

  3. $211.3 m^3$

  4. $3737 m^3$


Correct Option: A
Explanation:

Side of a cube$=7.203m$

                        $={(7.203)}^3$
                        $=373.714m^3$
$\therefore$  Volume of a cube $=373.7m^3$

In which of the following numbers, all zeros are significant?

  1. 5.0005

  2. 0.0030

  3. 30.000

  4. 0.5200


Correct Option: A
Explanation:

Any zeros between two significant digits are significant.

Non zero digits are always Significant.

  1. True

  2. False


Correct Option: A
Explanation:

Non zero digits are always significant it is a true statement.

Ex: $1234$ Total significant numbers are 4.

Calculate the following with due regard for significant figures:


 $\dfrac{1.53\times 0.9995}{1.592}$.

  1. $0.961$

  2. $0.921$

  3. $0.123$

  4. $0.913$


Correct Option: A
Explanation:

$1.53\times 0.9995=1.529=1.53$ .....By applying significant figure rule


$\cfrac { 1.53\times 0.9995 }{ 1.592 } =\cfrac { 1.53 }{ 1.592 } =0.961$

Hence, the correct option is $A$

If repeated measurements give values close to one another, the number is:

  1. surely precise

  2. surely accurate

  3. surely precise and accurate

  4. all of these are correct


Correct Option: A
Explanation:

Precision $=$ Individual value $-$ mean value

If the repeated measurement value is close to one another, the mean value will be close to the individual values. Therefore, their difference i.e. Precision is close to zero. Therefore, they are surely precise.
But the accuracy is the difference between the actual value & the mean value.
As we do not know the actual value, we cannot predict its accuracy.

The number of significant figures present in $4.50 \times 10^{3} $ is:

  1. 2

  2. 3

  3. 4

  4. 5


Correct Option: A
Explanation:
Number of significant figures present in $4.50 \times {10}^{3}$-
$4.50 \times {10}^{3} = 4500$
Thus, there are two significant figures.

Which of the following values possess maximum number of significent zeros?

  1. $0.00007$

  2. $0.00070$

  3. $20.000$

  4. $0.800$


Correct Option: C

After rounding off 1.235 and 1.225, we will have their answers respectively as 

  1. 1.23, 1.22

  2. 1.24 , 1.23

  3. 1.23 , 1.23

  4. 1.24 , 1.22


Correct Option: D

Which among the following measurements contains the highest number of significant figures? 

  1. $1.123 \times 10^{-3}kg$

  2. $1.2 \times 10^{-3}kg$

  3. $0.123 \times 10^{3}kg$

  4. $2 \times 10^{5}kg$


Correct Option: A

The correctly reported answer of the addition of 4.523, 2.3 and 6.24 will have significant figures

  1. 2

  2. 3

  3. 4

  4. 5


Correct Option: A

Which of the following has two significant figures?

  1. $0.070$

  2. $0.70$

  3. $7.0$

  4. $70$


Correct Option: A,B,C
Explanation:


Leading Zeroes are not significant because these zeroes only serve as space holder. They are there to put decimal point in correct location. Trailing zeroes in a number containing decimal point are significant.

Leading zeroes in whole number are never significant so 70 has only 1 significant figure.

So, option A, B and C are correct.

Which of the following have same significant figures?

  1. $6.02\times 10^{23}$

  2. $7.70\times 10^{-20}$

  3. $7.50$

  4. $0.75$


Correct Option: A,B,C
Explanation:

The number of single digits that are important in the coefficient of an expression in scientific notation is termed as significant number.


$(A),(B)$ & $(C)$ have $3$ significant figures.

Wheras, $(D)$ has only $2$ significant figures.

Statement I: The number $5,007$ has three significant figures
Because
Statement II: Zeros between non-zero digits are significant

  1. one is True, second is  True and currect expilanation

  2. one is true and second is true

  3. one is true  and second is False

  4. one is False and  second is True

  5. False False


Correct Option: D
Explanation:

 Statement I: The number $5,007$ has four significant figures
Because
Statement II: Zeros between non-zero digits are significant
Hence, the statement I is false and statement II is true.

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$14.5-3.46=$______

  1. $11$

  2. $10$

  3. $11.04$

  4. $11.0$

  5. $11.4$


Correct Option: D
Explanation:

      $14.5-3.46=11.04$

In subtraction, the final answer is written as the same number of decimal places as that of the term with the least number of decimal places.
  $\therefore$ The answer is $11.0$

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?


$2.8\times 8.96 = ? $

  1. $25.09$

  2. $25.1$

  3. $25$

  4. $25.08$

  5. $25.088$


Correct Option: B
Explanation:

In multiplication, the final answer is reported as the same number of decimal places as that of the term with the least number of decimal places.


$2.8\times 8.96=25.088=25.1$

Hence, the correct answer is option $B$.

How many significant digits does the measurement $0.5873g$ possess?

  1. $1$

  2. $2$

  3. $3$

  4. $4$

  5. $5$


Correct Option: D
Explanation:

The significant digits in the number $0.5873g$ are $5,8,7$ and $3$. Therefore, the number of significant digits in the given number are $4$.

Two samples were weighed using different balance and the following data were obtained.
Sample #1=3.719 grams
Sample #2=0.42 gram
The total mass of the samples should be reported as :

  1. 4 grams

  2. 4.1 grams

  3. 4.139 grams

  4. 4.14 grams

  5. 4.140 grams


Correct Option: D
Explanation:

After rounding off to $2$ significant digits, weight of sample $1$ can be reported as $3.72$ grams. Therefore, total mass $= (3.72+0.42)=4.14 $ grams.

What is the final significant digit in the measurement of $16.280g$?

  1. $1$

  2. $0$

  3. $8$

  4. $6$

  5. $2$


Correct Option: B
Explanation:

The significant digits in the number $16.280$ are $1,6,2,8$ and $0$. Therefore, the final significant digit in the given number is $0$.

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$\dfrac{12.55}{3.0} =4.18333$

  1. $4.18333$

  2. $4.2$

  3. $4.18$

  4. $4.183$

  5. 37.45


Correct Option: B
Explanation:

In multiplication, the final answer is reported as the same number of decimal places as that of the number with the least decimal places.

Therefore, $4.18333$ should be rounded off to only one decimal place.
Therefore, $\dfrac{12.55}{3.0}=4.2$

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$4.51\times{10}^{5}+3.6\times{10}^{3}$

  1. $4.55\times {10}^{5}$

  2. $8.11\times {10}^{5}$

  3. $4.546\times {10}^{5}$

  4. $8.11\times {10}^{8}$

  5. $4.5\times {10}^{5}$


Correct Option: E
Explanation:

In addition, the final product is reported as the same number of decimal places as that of the number with least decimal places.

$\therefore \quad 4.51\times { 10 }^{ 5 }+3.6\times { 10 }^{ 3 }=4.546\times { 10 }^{ 5 }$
                                                  $=4.5\times 10^5$

What is the molecular mass of glucose $C _6H _{12}O _6$ molecule up to 6 significant figures?

  1. 0180.16

  2. 180.16

  3. 180.1620

  4. 180.162


Correct Option: D
Explanation:

Molecular mass of glucose is $180.162$

Therefore, the molecular mass upto six significant figures is $180.162$.

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$(1.23\times {10}^{23})\times (3\times{10}^{14})=3.69\times {10}^{37}$

  1. $4\times {10}^{37}$

  2. $3.69\times {10}^{37}$

  3. $3.7\times {10}^{37}$

  4. $3.69\times {10}^{40}$

  5. $3.7\times {10}^{40}$


Correct Option: C

Which of the following is an exact number?

  1. 10.25 g

  2. 4.000 kg

  3. 7 chairs

  4. 60 seconds


Correct Option: C
Explanation:

Exact number is the number which does not have uncertainity in measurement and significant figures.

Therefore, $7$ chairs is an exact number.

Select the numbers with same significant figures:

  1. $6.02 \times 10^{23}$

  2. $0.25$

  3. $6.60 \times 10^{-34}$

  4. $1.50$


Correct Option: A,C,D
Explanation:

In $A:-$ Significant figures $=6,0,2 \Rightarrow 3$ figures

In $B:-$ Significant figures $=2,5 \Rightarrow 2$ figures
In $C:-$ Significant figure $=6,6,0 \Rightarrow 3$ figures
In $D:-$ Significant figures $=1,5,0 \Rightarrow 3$ figures
Therefore, $(A), (C)$ and $(D)$ have same significant figure.

In which of the following numbers, all the zeros are insignificant?

  1. 0.0010

  2. 0.00100

  3. 0.001000

  4. 0.001


Correct Option: D
Explanation:

All the last zero or trailing zero's in the decimal portion and between 2 significant digits only are significant.

Which set of figures will be obtained after rounding up the following upto three significant figures?
34.216,  0.04597, 10.4107

  1. 34.3, 0.0461, 10.4

  2. 34.2, 0.0460, 10.4

  3. 34.20, 0.460, 10.40

  4. 34.21, 4.597, 1.04


Correct Option: B
Explanation:

To round up a given number, ignore the last digit as such if the digit next to it is less than 5. Then increase it by 1, if the next digit is greater than 5.

(i) 34.216

34.22 { since next digit (6) is greater than 5 }

34.2 {since next digit (2) is less than 5 }

 (ii) 0.04597

0.0460 {since next digit (7) is greater than 5}

(iii) 10.4107

10.411 { since next digit (7) is greater than 5}

10.41 { since next digit (1) is less than 5}

10.4 { since next digit (1) is less than 5}

Thus option B is correct.

Few figures are expressed in scientific notation. mark the incorrect one.

  1. $234000 = 2.34 \times 10^5$

  2. $8008 = 8 \times 10^3$

  3. $0.0048 = 4.8 \times 10^{-3}$

  4. $500.0 = 5.00 \times 10^2$


Correct Option: B
Explanation:

Figures in scientific notation will be:

A. $234000=2.34 \times 10^5$ 

B. $8008=8.008 \times 10^3 $

C. $0.0048=4.8 \times 10^{−3}$

D. $500.0=5.00 \times 10^2$

Which of the following rules regarding the significant figures and calculations involving them is not correct?

  1. The result of an addition or subtraction is reported to the same number of decimal places as present in number with least decimal places.

  2. Result of multiplication or division should have same number of significant figures as present in most precise figure

  3. The result of multiplication or division should be rounded off to same number of significant figures as present in least precise figure.

  4. The non-significant figures in the measurements are rounded off.


Correct Option: B
Explanation:
1. The result of an addition or subtraction is reported to the same number of decimal places as present in number with the least decimal places.
2. The result of multiplication or division should be rounded off to the same number of significant figures as present in number with the least significant number.
3. The result of multiplication or division should be rounded off to the same number of significant figures as present in the least precise figure.
4. The non-significant figures in the measurements are rounded off.
option B is correct

Magnitude of $e/m$ for ${O^ - }$

  1. $10^{-12}$

  2. $10^{-20}$

  3. $10^{-22}$

  4. $10^{-18}$


Correct Option: B
Explanation:

Here: Mass of ${O^ - } = 16\,g/mol$ and

charge ${O^ - } = {\text{one unit}}$

$ = 1.6 \times {10^{ - 19}}C$

So,

$e/m = \dfrac{{{\text{Charge}}}}{{{\text{Mass}}\,{\text{ratio}}}}$

$ = \dfrac{{1.6 \times {{10}^{ -19}}C}}{{16\,g/mol}}$

$ = \dfrac{{1.6 \times {{10}^{ - 19}}\times C \times mol}}{{16\,g}}$

$ = \dfrac{{0.1 \times {{10}^{ - 19}}\times C \times NA}}{g}\,\,\,\,\,\,\,\,\,\boxed{mol = NA}$

$e/m = {10^{ - 20}}\dfrac{C}{g}$

Two students are working on an AP Chemistry lab. Their assignment is to determine experimentally the density of a nonvolatile organic liquid, limestone. The accepted value for the density of limestone is $0.8422\ g/mL$. Each student conducts three separate density determinations, then calculates a mean (average) value for the density and the standard deviation for their three trials.

Student A Student B
Density #$1$ $0.8421 g/mL$ $0.8408 g/mL$
Density #$2$ $0.8514 g/mL$ $0.8502 g/mL$
Density #$3$ $0.8355 g/mL$ $0.8332 g/mL$
Mean Density $0.8430 g/mL$ $0.8414 g/mL$
Standard Deviation $0.0080$ $0.0085$

The results and calculations for each students are shown in the table below.
Of the four descriptions given below, which BEST interprets the accuracy and precision of Student A and Student B?

  1. Student A and Student B are equally precise, but Student B has more accurate results.

  2. Student A and Student B are equally accurate, but Student B has more precise results.

  3. Student A and Student B have equal accuracy and equal precision.

  4. Student A has more accurate and more precise results than Student B.


Correct Option: B
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